scholarly journals Nonlinear perturbations of a p(x)-Laplacian equation with critical growth in RN

2013 ◽  
Vol 287 (8-9) ◽  
pp. 849-868 ◽  
Author(s):  
Claudianor O. Alves ◽  
Marcelo C. Ferreira
Keyword(s):  
Critical Growth ◽  
Nonlinear Perturbations ◽  
Laplacian Equation

On perturbations of a class of a periodic m-Laplacian equation with critical growth

2001 ◽  
Vol 45 (7) ◽  
pp. 849-863 ◽  
Author(s):  
C.O. Alves ◽  
João Marcos do Ó ◽  
O.H. Miyagaki
Keyword(s):  
Critical Growth ◽  
Laplacian Equation

scholarly journals Multiplicity of normalized solutions for p-Laplacian equation with critical growth in RN

2021 ◽  
Author(s):  
Xueqin Peng
Keyword(s):  
Lagrange Multiplier ◽  
Unknown Parameter ◽  
Critical Growth ◽  
Laplacian Equation ◽  
Normalized Solutions

In this paper, we consider the following p-Laplacian equation      −∆pu + |u|p−2u − λu = µ|u|q−2u + |u|p∗−2u, in RN, u > 0, ∫ RNu2dx = a2, where a,µ > 0, −∆pu = div(|∇u|p−2∇u),1 < p < N, λ ∈ R is an unknown parameter that appears as a Lagrange multiplier, p < q

scholarly journals Ground-State Solutions for a Class ofN-Laplacian Equation with Critical Growth

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Guoqing Zhang ◽  
Jing Sun
Keyword(s):  
Ground State ◽  
Critical Growth ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Ground State Solutions ◽  
Laplacian Equation

We investigate the existence of ground-state solutions for a class ofN-Laplacian equation with critical growth inℝN. Our proof is based on a suitable Trudinger-Moser inequality, Pohozaev-Pucci-Serrin identity manifold, and mountain pass lemma.

scholarly journals On Dirichlet problem for fractional p-Laplacian with singular non-linearity

2016 ◽  
Vol 8 (1) ◽  
pp. 52-72 ◽  
Author(s):  
Tuhina Mukherjee ◽  
Konijeti Sreenadh
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Smooth Boundary ◽  
Critical Growth ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

Abstract In this article, we study the following fractional p-Laplacian equation with critical growth and singular non-linearity: (-\Delta_{p})^{s}u=\lambda u^{-q}+u^{\alpha},\quad u>0\quad\text{in }\Omega,% \qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega, where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega} , {n>sp} , {s\in(0,1)} , {\lambda>0} , {0<q\leq 1} and {1<p<\alpha+1\leq p^{*}_{s}} . We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ.

On nonlinear perturbations of a periodic elliptic problem in involving critical growth

2004 ◽  
Vol 56 (5) ◽  
pp. 781-791 ◽  
Author(s):  
C.O. Alves ◽  
João Marcos do Ó ◽  
O.H. Miyagaki
Keyword(s):  
Elliptic Problem ◽  
Critical Growth ◽  
Nonlinear Perturbations

On a zero-mass (N,q)-Laplacian equation in RN with exponential critical growth

2021 ◽  
Vol 213 ◽  
pp. 112488
Author(s):  
J.L. Carvalho ◽  
G.M. Figueiredo ◽  
M.F. Furtado ◽  
E. Medeiros
Keyword(s):  
Critical Growth ◽  
Laplacian Equation ◽  
Zero Mass ◽  
Exponential Critical Growth

scholarly journals Nonlinear Perturbations of a Periodic Elliptic Problem with Critical Growth

2001 ◽  
Vol 260 (1) ◽  
pp. 133-146 ◽  
Author(s):  
Claudianor Oliveira Alves ◽  
Paulo Cesar Carrião ◽  
Olimpio Hiroshi Miyagaki
Keyword(s):  
Elliptic Problem ◽  
Critical Growth ◽  
Nonlinear Perturbations
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